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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 54450d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54450.z2 | 54450d1 | \([1, -1, 0, -21281442, 18808653716]\) | \(1469878353/640000\) | \(464114844019530000000000\) | \([2]\) | \(6082560\) | \(3.2373\) | \(\Gamma_0(N)\)-optimal |
54450.z1 | 54450d2 | \([1, -1, 0, -165029442, -802998662284]\) | \(685429074513/12500000\) | \(9064743047256445312500000\) | \([2]\) | \(12165120\) | \(3.5839\) |
Rank
sage: E.rank()
The elliptic curves in class 54450d have rank \(1\).
Complex multiplication
The elliptic curves in class 54450d do not have complex multiplication.Modular form 54450.2.a.d
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.